Question

the profit that a vendor makes per day by selling x pretzels is given by the function:

P(x)=-0.004x^2 +2.4x -100
Find the number of pretzels that must be solved to maximize profit.

Answer 1

do you have a graphing calculator?
You can just plug it in and find the max...

Answer 2

can't use a graphing calculator in this class

Answer 3

But it's a calculus class, right?

Answer 4

pre-calc

Answer 5

You're calculating derivatives?

Answer 6

Vertex of a parabola can be used in place of a derivative for quadratic functions.

Answer 7

x=-b/(2a) will tell you where the max is given a quadratic of the form ax^2+bx+c.
Once you get the x value, plug it back into your function to get the y value (the maximum).

Answer 8

right, would I be able to just use the formula \[y= (4(ac)-b^{2}) \div 2(a)\]

Answer 9

I haven't seen that... but it looks like part of the quadratic formula (kind-of).

Answer 10

@refusetofail What @EulerGroupie meant is, plug the x-value you get back into your equation (\(P(x)=-0.004x^2 +2.4x -100\)), to get the y-value.

Answer 11

It doesn't get the right answer, and we aren't really looking for the y value now that I look closely... we want the number of pretzels that will lead to the maximum... so the x value is your full answer.

Answer 12

Oh, you're right.

Answer 13

\[x=-\frac{b}{2a}\]should do it.

Answer 14

yeah! that makes sense, cause the formula I put up there was a shortcut for gettting the y-value (though it should've been 4a not 2a), but the y-value didnt match the answer in the textbook.

Answer 15

oh cool, with your change, I did get the max that I found through my method... something new! Thank you.

Answer 16

no prob :)